Question

23. X and Y are two points with position vectors 3 a + b and a - 3b respectively. Write the
position vector of a point Z which divides the line segment XY in the ratio 2:1 externally.​

Answer 1

Therefore the position vector of Z is$=5(\vec{a}+\vec{b})$

Step-by-step explanation:

Given that ,

X and Y are two points with position vector $3\vec{a}+\vec{b}$ and $\vec{a}-3\vec{b}$ respectively.

If  C divides the line which is joining by two vector  $\vec{A}$ and $\vec{B}$ in the ratio m:n externally.

Then the position  of C is$\frac{m\vec{B} -n\vec{A}}{m-n}$

Therefore the position vector of Z is $\frac{2(3\vec{a}+\vec{b})-1(\vec{a}-3\vec{b})}{2-1}$ $=5(\vec{a}+\vec{b})$